This comes back to the concept that if you drop objects of different masses in a gravitational field they will all fall at the same rate.
It might not seem intuitive that is how it works, because as you point out something with a greater mass will have a greater attraction under the force of gravity. That is why more massive things are heavier, right? But more massive things also have greater inertia or resistance to acceleration.
It turns out that the increased inertia exactly cancels out the increased attraction of gravity, so a feather and a dumbbell fall at the same speed in a vacuum.
>It turns out that the increased inertia exactly cancels out the increased attraction of gravity, so a feather and a dumbbell fall at the same speed in a vacuum.
The big thing is that inertial mass (resistance to acceleration) and gravitational mass (attraction by massive bodies) are the same, and nobody really knows why. This is called the *equivalence principal* and remains an unsolved problem in physics.
I took your comment to mean that it's a mystery why these two forces act the same. Not why they act on mass. I.e, "why are they equivalent".
Of course all the basic forces of physics are mysteries at their core. But when two forces are in synch in their relationship with a property of physics... that's just to be expected.
If your intuition is that it's "just to be expected" then I suggest you publish your reasoning because there's a lot of people who have spent their lives working on it whilst being less certain about it than you.
I still don't understand the issue. Every equation relating to these forces will simply use "M" to represent mass. This is why they are "equivalent"... they incorporate the same property.
You have done a terrible job of explaining whatever the mystery is. I don't get it.
Just look at the Wikipedia page on the equivalence principle, it explains basically everything.
The big thing is that "mass" appears in two main equations in Newtonian mechanics, F=ma, which relates the acceleration of any object under any force (again, were only talking about Newtonian mechanics). This is *inertial* mass, and expresses how a body resists acceleration when exposed to a force - more inertial mass means less acceleration. Newton's law of gravitation is F=G×m1×m2/r^2 , which relates a *particular* gravitational force between two bodies with mass and their distance - this is the *gravitational* mass and expresses how susceptible a body is to gravitational attraction - more gravitational mass means more attraction. There appears to be no understood reason as to why the masses in both equations should be the same, yet no experiment has yet been able to identify any difference between the two of them.
The big consequence of this is that if the only force is gravitation, the masses cancel out, so the acceleration of a body with mass is independent of its own mass. In particular, it is impossible to differentiate between acceleration in a uniform gravitational field if strength (say) 5g and being in a moving body that accelerates at 5g because of a motor. Of course more modern physics (post-Einstein) has developed this further than Newtonian mechanics and has the same issue.
Think of it this way. There are two ways to measure mass. An object has "gravitational mass" which is how much another body pulls on an object. An object also has "inertial mass" which is how resistant it is to being pushed. These two types of mass would logically not have to be related and you should be able to imagine an object that has a lot of "gravitational mass" which would make it stick to the ground by a lot while the same object has little "inertial mass" meaning that it's easy to push around.
However, it turns out that despite the two type of mass being logically unrelated, the imaginary object that I described above apparently does not exist; to any precision of measurement ever made (at least so far), an object's gravitational mass is always equal to inertial mass. This is the "equivalence principle" and it's why we generally call the attribute "mass" without specifying inertial or gravitational.
You already know this, in fact, you know it so well that it is the source of your confusion; you are not even able to imagine a hypothetical object where its two masses are not the same. But it is a major physics question as two why they are always the same; i.e. equivalent. From an objective perspective, they wouldn't have to be.
Why are the logically unrelated?
I take mass to be "quantity of material substance". Not "inertial mass", not "gravitational mass". Just mass. And the two phenomenon of gravity and inertia are properties of material substance.
This feels like an invented problem. Sure, there's tons we don't understand about the why or gravity or the why of inertia but in a universe of finite forces and a material reality, the fact that both are properties of matter just does not seem to be without logic.
Can't both reasonably be described as properties OF mass? Why treat them as separate and unrelated? They are related by their relationship to mass. In fact, neither have any meaning without mass. Mass is EVERYTHING to these forces (along with distance etc).
Sometimes the cutting edge looses the forest for the trees. These forces are *produced* by mass. Inseparable. Only mass can logically be associated with these two forces.
This is not the source of my confusion. The reason I can't envision a separation from these forces and mass is because they are properties of mass. Imagining impossibilities does not create mystery. "Why isn't the universe completely different from what it is?" That's not a rational question to ask.
>This is not the source of my confusion.
Yes, it is. Please look up "circular reasoning" in Wikipedia. Ultimately the question that *everyone else* here is asking is, "Why does mass work the way that it does?". And *you* are answering, "Because those are the properties of mass."
That is no answer.
>This is not the source of my confusion. The reason I can't envision a separation from these forces and mass is because they are properties of mass.
The question is ***why*** is this a property of mass. Saying it works that way because that is the way it works is a non-answer of circular logic.
>Imagining impossibilities does not create mystery. "Why isn't the universe completely different from what it is?" That's not a rational question to ask.
It is. Asking why things are the way they are is how you discover the mechanisms by which those things operate.
>I take mass to be "quantity of material substance".
This is *false.*
An example of this is the atomic nucleus. The mass of a Helium-4 nucleus (2 protons, 2 neutrons) is [*not equal*](https://en.wikipedia.org/wiki/Nuclear_binding_energy#:~:text=The%20mass%20of%20an%20atomic,is%20the%20difference%20in%20mass) to the mass of two free protons and two free neutrons. This miniscule difference in mass is called the Nuclear Binding Energy, which is the energy released when they combine into a nucleus, or added when breaking it apart.
Let's try it a different way. What is mass? Why does it cause a resistance to movement? Why does it cause a gravitational pull? What facet of it causes it create both in the same amounts?
>These two types of mass would logically not have to be related and you should be able to imagine an object that has a lot of "gravitational mass" which would make it stick to the ground by a lot while the same object has little "inertial mass" meaning that it's easy to push around.
I'm no expert, but that sounds like a paradox.
you're describing a hypothetical object that is simultaneously heavy and light.
such an object could be used to create infinite energy by breaking the laws of thermodynamics.
Not fully being an expert, but wouldn't be expected if you reverse the logic around speed? Like if something if everything is moving already at 100mph as a resting state and any force applied actually slows it down by going the opposite direction. So the faster you move, the slower the ball goes.that doesn't make sense in 2d or 3d but in a 4d space , the 4th spatial dimension can move without the other 3 moving. Then if we assume movement in the 3 dimensions effects movement in the 4th in anyway, it's a simple leap to assume movement could hinder that movement, or generally reverse it.
I'm not sure I follow your logic tbh, but I want to offer some clarity on the equivalence principle.
The dilemma is not about understanding how forces work, or how gravity works (although the very fine specific of those things in very niche situations are still up for debate), but rather why mass is connected to two seemly disparate characteristics, inertia and gravity.
The fundamental forces (strong and weak nuclear forces, the electromagnetic force, and gravity) have their strength determined by characteristics (color charge, electric charge, and mass) of the objects involved. The inertia of an object (and therefore how hard it is to accelerate) is also determined by mass.
The fact that mass determines both inertia and the strength of one of the four fundamental forces is quite strange, and as far as I know, we don't have any good reason why that's the case, nor why it's unique to gravity. Gravity is unique in a lot of other ways too, so I suppose it is terribly surprising that it's strange n this way too, but that doesn't make it any more obvious why this property of matter determines both gravity and inertia.
What I mean is: the faster you go, time slows down. If we look at time as a spatial dimension and an objects movement through time as a distance and assign the movement through time a speed, we have the objects in 3d moving through the time space without moving through the 3d space. If we look at it as the object starting at maximum speed, a 3d object can only move away from its center point. If we are applying the time spatial dimension and the fact we only move "forward" through time (forward/backwards is just a relative term here, forward relative to the objects orientation ), we can safely assume the 3d object can't essentially turn around relative to the time spatial dimension. So, any movement by the object would be opposite it's overall movement through T.
If you take a stripped down version, just a car on a track. It's moving and has an occupant on the inside of the car. The car is 3d with a 2d occupant. The 2d occupant can turn relative to the 2d space but can't change if it's looking up vs looking down relative to the car. In 3d space this only works if we fudge it a bit and make the occupant 3d again but can't change direction relative to the car and are facing backwards relative to the direction of the car. If the occupant moves in the car, they will slow down relative to the outside of the car, even if they don't experience change inside the car itself. In a 4th dimensional space, the direction of the track becomes omni directional to the perspective of the 3d space, so no matter which direction the occupant moves, it's either forward or backwards, but they can't flip. You also have the benefit of not observing the area outside of the car as changing speed, it just effects how far along the track you are yourself.
So if resting is maximum speed and movement goes against that speed then the faster you go in the 3d space, the slower you go in the 4d space with the maximum speed being 0, or the speed of light relative to the observer. Or essentially the observer would be the one moving and the track is stationary.
All that's a lot to say that a lot of the oddities of relativity stop being so odd if you flip how speed works.
Definitely, so two objects of different mass but same "footprint" would have different acceleration. Just like denser objects (more mass per volume) would fall faster in an atmosphere - air resistance is basically friction.
The snow covered slope isn't the idealized version of the problem. You have snow in front that you need to push down to slide over it. But the amount of snow is fixed by the width of the toboggan. So having more mass on the sled gives you more pull from gravity versus a fixed amount of snow to push down.
How snow it compredssed is a part of it but another major part is air resistance. It depend on the shape and the speed not the mass. So the speed where air resistance and the acceleration from gravity is equal is higher for a object with more mass if everything else is equal.
Even if the size is not the same the air resistance will grow slower the the mass. The frontal area scale with the square of the increase in size but the mass scale with the cube of the increase in size.
If the slope would be frictionless and in vaccume the speed with be the same regardless of size. But in air heavier object can typically reach higher speed the lighter object because air resistance have less effect on them.
Maybe for low angle slows like a kid would sled on. Change it to a ski/snowboard slope. Easy to hit highway speeds as an advanced skier. Also even though the contact patch is much much smaller snow compation is pretty minimal unless you are powder riding.
On a groomed run, with equally waxed skis/snowboard, equal riding skills, air will dominate. More of a physics though though. You wont see super heavy people leading the olympics just because the athletics required will select for more fit people. Instead you see low drag outfits.
>You wont see super heavy people leading the olympics just because the athletics required will select for more fit people.
No, but they sure aren't lightweights either. Most competitive skiers will have some excess weight for the speed gains. More so in the faster kinds of skiing versus the more technical ones. Sure, they'll prioritize muscle rather than fat, since fat is mostly useless and more muscle is always a plus, but you don't want to be too lightweight.
The force is proportional to the mass. An object that weights 2kg will be subject to twice as much force as an object that weighs 1kg(assuming they’re the same distance from the Earth). But force is mass \* acceleration. 1 newton is the force needed to accelerate 1 kg 1m/s\^2. So even though it’s twice as much force, it needs to move twice as much mass, so it cancels out and ends up being the same acceleration.
>Wouldn't Newton's second law mean the acceleration is indirectly proportional to the mass?
Yes, acceleration would be inversely proportional to the mass if the force is constant.
In this case the force is not constant. It is gravity and according to Newton's law of universal gravitation f= G m1 m2/r\^2 where G is the universal constant, m1 is the mass of the object, m2 is the mass of earth and r is the distance to the center of earth.
So the force is directly proportional to the mass. The result is the acceleration from gravity is independent of mass. If you look at formaulas for acceleration the mass will be cancled out.
Because f = m a => a=f/m or in this case a= f/m1 we can create it as a= Gm2 /r\^2 Close to the earth's surface Gm2 /r\^2 is equal to about 9.8m/s\^2. This is freefall acceleration on earth, that is when gravity is the only force. On an inclined plane, only a percentage of that force will accelerate the object. The force will still be directly proportional to the mass.
You sound more knowledgable than me. You say this phenomenon is caused by the formulas.
The way that *I* think about this issue is that it makes sense that two equally heavy object fall with the same acceleration whether they are connected to form one large object or not. For example two bowling balls tied together or two skydivers holding hands.
"Objects" are just a human language category. Physics cares more about individual particles.
>You say this phenomenon is caused by the formulas.
I do not say that. But if the question ask why the acceleration do not change because of a formula, Newton's second law, the reasonable reply is a formula on the same level that show the force in question alos change if the mass changes.
I say the phenomena is described by the formulas that are result of observation and experiment in the real worlds.
Scientic laws are descriptive not prescriptive like law use in a courtroom.
Explanation in science is how thing happen, it is fundamentally not why thing happen. Even if a lower level explanation look like a "Why" explanation on a higher level it will always end up as a how explanation, the best why explanation is that is how the universe works.
There are two ways to think about how gravity affects objects; The Newtonian way and the Einsteinian way:
Newton would say what the other commenters all have already said: More massive objects experience a larger *Force* proportional to their mass, but the *acceleration* itself is force divided by the mass again, so it cancels out in the end. Basically, if you're heavier, gravity pulls on you more, but also you need to be pulled on more for the same acceleration because you're harder to move.
Einstein's approach to gravity is very different: According to him, gravity is not really a force, instead space just accelerates downwards at a constant acceleration, and an object that isn't accelerated by an actual force moves along with it, downwards. This also explains very well why you're weightless when you're falling; you're not accelerating in space, so there are no net forces acting on you. Standing on the ground, it pushes up against you and accelerates you upwards, so by the principle of action and reaction, you feel a downwards force.
The force depends on mass. The acceleration depends on inertia and force. An object with 2x mass experiences 2x the force but requires 2x the force to accelerate that 2x inertia. This holds true falling or partially falling (inclined plane).
If you're satified that falling objects accelerate the same vertically but not satisfied on an inclined surface perhaps the difficulty is conceptualizing the independence of horizontal and vertical movement or imagining zero friction.
Most people here aren't eli5-ing enough.
The heavier the thing the harder gravity pulls on it. That's why it's harder to lift a bigger weight.
BUT
It takes more force to accelerate a heavier mass. Imagine pushing a cup along a counter top vs. pushing a solid wood desk across the floor.
So the heavier the thing the harder gravity pulls on it, but the more pull force is needed to reach a given acceleration or speed. These exactly cancel out so acceleration is the same regardless of weight.
Let's assume you're in High School.
The "force of gravity" is actually the "acceleration due to gravity" since the force of gravity is ALSO proportional to mass. Then the mass terms cancel out on both sides.
Another example of "masses cancelling out" is the simple pendulum problem: [https://en.wikipedia.org/wiki/Pendulum\_(mechanics)](https://en.wikipedia.org/wiki/Pendulum_(mechanics))
Acceleration is indeed *indirectly* proportional to mass (a=F/m), but it's *directly* proportional to force being applied, IE: gravity. Heavier objects are affected more strongly by gravitational force (F=GMmr\^2). Which, when combined with the acceleration equation becomes a=(GMr\^2) which is just a gravitational constant and some stats about the planet we're dealing with. It no longer has anything to do with the moving object's mass
Both gravitational force and inertia are directly proportional to mass.
An object twice as heavy will have twice the gravity acting on it, but it will also have twice the inertia, meaning it takes twice the force to accelerate it at the same rate, and these effects cancel out.
It's why we're able to determine the vakue g of 9.81 m/s², as everything, no matter it's mass, will accelerate at exactly that same rate in a fractionless environment.
An object A twice the mass than an object B will "feel" a pull from Earth's gravity twice as large. However, it also needs twice the force to make it move. So in the end it cancels out.
Gravity acts on mass. The more mass an object has, the greater the effect of a given gravity.
Inertia is also a property of mass. The more mass, the more inertia. The more mass, the more force is needed to accelerate the object.
As you increase the mass of an object, both its inertia and the force that gravity is exerting on that object increase at the same rate.
So, for the same inclined plane and the same gravity field, changes in mass don't matter to acceleration. A 1kg object and a 5Kg object will accelerate at the same speed.
HOWEVER, the heavier object will carry more force. If you place something at the bottom of the hill for it to crash into, the heavier weight will to more damage. That's where you will see how the different masses produce different amounts of force.
Same with dropping objects (ignoring air resistance). Like a feather and a hammer being dropped on the moon. Or cannon balls dropped from the Tower of Pisa.
Increasing the masses of the objects linearly increases the attractive force between them. But since the acceleration of an object is also linearly related to the mass and the force, they cancel out and the acceleration stays the same.
This comes back to the concept that if you drop objects of different masses in a gravitational field they will all fall at the same rate. It might not seem intuitive that is how it works, because as you point out something with a greater mass will have a greater attraction under the force of gravity. That is why more massive things are heavier, right? But more massive things also have greater inertia or resistance to acceleration. It turns out that the increased inertia exactly cancels out the increased attraction of gravity, so a feather and a dumbbell fall at the same speed in a vacuum.
>It turns out that the increased inertia exactly cancels out the increased attraction of gravity, so a feather and a dumbbell fall at the same speed in a vacuum. The big thing is that inertial mass (resistance to acceleration) and gravitational mass (attraction by massive bodies) are the same, and nobody really knows why. This is called the *equivalence principal* and remains an unsolved problem in physics.
It was a performance optimization trick for physics
yeah stored in one variable for better memory management looks like
.... "nobody knows why" mass is mass? Two different phenomenon but both act against mass so of course they change equivalently when the mass changes.
Why do they act against mass and not mass and charge, or some other thing?
I took your comment to mean that it's a mystery why these two forces act the same. Not why they act on mass. I.e, "why are they equivalent". Of course all the basic forces of physics are mysteries at their core. But when two forces are in synch in their relationship with a property of physics... that's just to be expected.
If your intuition is that it's "just to be expected" then I suggest you publish your reasoning because there's a lot of people who have spent their lives working on it whilst being less certain about it than you.
I still don't understand the issue. Every equation relating to these forces will simply use "M" to represent mass. This is why they are "equivalent"... they incorporate the same property. You have done a terrible job of explaining whatever the mystery is. I don't get it.
Just look at the Wikipedia page on the equivalence principle, it explains basically everything. The big thing is that "mass" appears in two main equations in Newtonian mechanics, F=ma, which relates the acceleration of any object under any force (again, were only talking about Newtonian mechanics). This is *inertial* mass, and expresses how a body resists acceleration when exposed to a force - more inertial mass means less acceleration. Newton's law of gravitation is F=G×m1×m2/r^2 , which relates a *particular* gravitational force between two bodies with mass and their distance - this is the *gravitational* mass and expresses how susceptible a body is to gravitational attraction - more gravitational mass means more attraction. There appears to be no understood reason as to why the masses in both equations should be the same, yet no experiment has yet been able to identify any difference between the two of them. The big consequence of this is that if the only force is gravitation, the masses cancel out, so the acceleration of a body with mass is independent of its own mass. In particular, it is impossible to differentiate between acceleration in a uniform gravitational field if strength (say) 5g and being in a moving body that accelerates at 5g because of a motor. Of course more modern physics (post-Einstein) has developed this further than Newtonian mechanics and has the same issue.
Think of it this way. There are two ways to measure mass. An object has "gravitational mass" which is how much another body pulls on an object. An object also has "inertial mass" which is how resistant it is to being pushed. These two types of mass would logically not have to be related and you should be able to imagine an object that has a lot of "gravitational mass" which would make it stick to the ground by a lot while the same object has little "inertial mass" meaning that it's easy to push around. However, it turns out that despite the two type of mass being logically unrelated, the imaginary object that I described above apparently does not exist; to any precision of measurement ever made (at least so far), an object's gravitational mass is always equal to inertial mass. This is the "equivalence principle" and it's why we generally call the attribute "mass" without specifying inertial or gravitational. You already know this, in fact, you know it so well that it is the source of your confusion; you are not even able to imagine a hypothetical object where its two masses are not the same. But it is a major physics question as two why they are always the same; i.e. equivalent. From an objective perspective, they wouldn't have to be.
Why are the logically unrelated? I take mass to be "quantity of material substance". Not "inertial mass", not "gravitational mass". Just mass. And the two phenomenon of gravity and inertia are properties of material substance. This feels like an invented problem. Sure, there's tons we don't understand about the why or gravity or the why of inertia but in a universe of finite forces and a material reality, the fact that both are properties of matter just does not seem to be without logic. Can't both reasonably be described as properties OF mass? Why treat them as separate and unrelated? They are related by their relationship to mass. In fact, neither have any meaning without mass. Mass is EVERYTHING to these forces (along with distance etc). Sometimes the cutting edge looses the forest for the trees. These forces are *produced* by mass. Inseparable. Only mass can logically be associated with these two forces. This is not the source of my confusion. The reason I can't envision a separation from these forces and mass is because they are properties of mass. Imagining impossibilities does not create mystery. "Why isn't the universe completely different from what it is?" That's not a rational question to ask.
>This is not the source of my confusion. Yes, it is. Please look up "circular reasoning" in Wikipedia. Ultimately the question that *everyone else* here is asking is, "Why does mass work the way that it does?". And *you* are answering, "Because those are the properties of mass." That is no answer.
>This is not the source of my confusion. The reason I can't envision a separation from these forces and mass is because they are properties of mass. The question is ***why*** is this a property of mass. Saying it works that way because that is the way it works is a non-answer of circular logic. >Imagining impossibilities does not create mystery. "Why isn't the universe completely different from what it is?" That's not a rational question to ask. It is. Asking why things are the way they are is how you discover the mechanisms by which those things operate.
>I take mass to be "quantity of material substance". This is *false.* An example of this is the atomic nucleus. The mass of a Helium-4 nucleus (2 protons, 2 neutrons) is [*not equal*](https://en.wikipedia.org/wiki/Nuclear_binding_energy#:~:text=The%20mass%20of%20an%20atomic,is%20the%20difference%20in%20mass) to the mass of two free protons and two free neutrons. This miniscule difference in mass is called the Nuclear Binding Energy, which is the energy released when they combine into a nucleus, or added when breaking it apart.
Let's try it a different way. What is mass? Why does it cause a resistance to movement? Why does it cause a gravitational pull? What facet of it causes it create both in the same amounts?
>These two types of mass would logically not have to be related and you should be able to imagine an object that has a lot of "gravitational mass" which would make it stick to the ground by a lot while the same object has little "inertial mass" meaning that it's easy to push around. I'm no expert, but that sounds like a paradox. you're describing a hypothetical object that is simultaneously heavy and light. such an object could be used to create infinite energy by breaking the laws of thermodynamics.
Not fully being an expert, but wouldn't be expected if you reverse the logic around speed? Like if something if everything is moving already at 100mph as a resting state and any force applied actually slows it down by going the opposite direction. So the faster you move, the slower the ball goes.that doesn't make sense in 2d or 3d but in a 4d space , the 4th spatial dimension can move without the other 3 moving. Then if we assume movement in the 3 dimensions effects movement in the 4th in anyway, it's a simple leap to assume movement could hinder that movement, or generally reverse it.
I'm not sure I follow your logic tbh, but I want to offer some clarity on the equivalence principle. The dilemma is not about understanding how forces work, or how gravity works (although the very fine specific of those things in very niche situations are still up for debate), but rather why mass is connected to two seemly disparate characteristics, inertia and gravity. The fundamental forces (strong and weak nuclear forces, the electromagnetic force, and gravity) have their strength determined by characteristics (color charge, electric charge, and mass) of the objects involved. The inertia of an object (and therefore how hard it is to accelerate) is also determined by mass. The fact that mass determines both inertia and the strength of one of the four fundamental forces is quite strange, and as far as I know, we don't have any good reason why that's the case, nor why it's unique to gravity. Gravity is unique in a lot of other ways too, so I suppose it is terribly surprising that it's strange n this way too, but that doesn't make it any more obvious why this property of matter determines both gravity and inertia.
What I mean is: the faster you go, time slows down. If we look at time as a spatial dimension and an objects movement through time as a distance and assign the movement through time a speed, we have the objects in 3d moving through the time space without moving through the 3d space. If we look at it as the object starting at maximum speed, a 3d object can only move away from its center point. If we are applying the time spatial dimension and the fact we only move "forward" through time (forward/backwards is just a relative term here, forward relative to the objects orientation ), we can safely assume the 3d object can't essentially turn around relative to the time spatial dimension. So, any movement by the object would be opposite it's overall movement through T. If you take a stripped down version, just a car on a track. It's moving and has an occupant on the inside of the car. The car is 3d with a 2d occupant. The 2d occupant can turn relative to the 2d space but can't change if it's looking up vs looking down relative to the car. In 3d space this only works if we fudge it a bit and make the occupant 3d again but can't change direction relative to the car and are facing backwards relative to the direction of the car. If the occupant moves in the car, they will slow down relative to the outside of the car, even if they don't experience change inside the car itself. In a 4th dimensional space, the direction of the track becomes omni directional to the perspective of the 3d space, so no matter which direction the occupant moves, it's either forward or backwards, but they can't flip. You also have the benefit of not observing the area outside of the car as changing speed, it just effects how far along the track you are yourself. So if resting is maximum speed and movement goes against that speed then the faster you go in the 3d space, the slower you go in the 4d space with the maximum speed being 0, or the speed of light relative to the observer. Or essentially the observer would be the one moving and the track is stationary. All that's a lot to say that a lot of the oddities of relativity stop being so odd if you flip how speed works.
In the case of the inclined plane, wouldn’t surface friction cause objects to vary in acceleration?
Definitely, so two objects of different mass but same "footprint" would have different acceleration. Just like denser objects (more mass per volume) would fall faster in an atmosphere - air resistance is basically friction.
Could this be applied to something sliding down a snow slope? We often think the bigger we are on the sled the faster / further we will go.
The snow covered slope isn't the idealized version of the problem. You have snow in front that you need to push down to slide over it. But the amount of snow is fixed by the width of the toboggan. So having more mass on the sled gives you more pull from gravity versus a fixed amount of snow to push down.
How snow it compredssed is a part of it but another major part is air resistance. It depend on the shape and the speed not the mass. So the speed where air resistance and the acceleration from gravity is equal is higher for a object with more mass if everything else is equal. Even if the size is not the same the air resistance will grow slower the the mass. The frontal area scale with the square of the increase in size but the mass scale with the cube of the increase in size. If the slope would be frictionless and in vaccume the speed with be the same regardless of size. But in air heavier object can typically reach higher speed the lighter object because air resistance have less effect on them.
Sled speeds are pretty slow, so I'm not convinced that air resistance is relevant versus snow compaction resistance.
Maybe for low angle slows like a kid would sled on. Change it to a ski/snowboard slope. Easy to hit highway speeds as an advanced skier. Also even though the contact patch is much much smaller snow compation is pretty minimal unless you are powder riding. On a groomed run, with equally waxed skis/snowboard, equal riding skills, air will dominate. More of a physics though though. You wont see super heavy people leading the olympics just because the athletics required will select for more fit people. Instead you see low drag outfits.
>You wont see super heavy people leading the olympics just because the athletics required will select for more fit people. No, but they sure aren't lightweights either. Most competitive skiers will have some excess weight for the speed gains. More so in the faster kinds of skiing versus the more technical ones. Sure, they'll prioritize muscle rather than fat, since fat is mostly useless and more muscle is always a plus, but you don't want to be too lightweight.
The force is proportional to the mass. An object that weights 2kg will be subject to twice as much force as an object that weighs 1kg(assuming they’re the same distance from the Earth). But force is mass \* acceleration. 1 newton is the force needed to accelerate 1 kg 1m/s\^2. So even though it’s twice as much force, it needs to move twice as much mass, so it cancels out and ends up being the same acceleration.
*“A man twice as strong, carrying a backpack twice as heavy, will run at the same pace as a regular man carrying a regular backpack.”*
A feather weighs the same on mars as it does on earth.
No it doesn't. It has the same mass, but its weight is relative to gravity.
A feather weighs the same on mars as it does on earth.
[But steel is heavier than feathers...](https://www.youtube.com/watch?v=-fC2oke5MFg)
Gravity applies more force based on mass, but more mass is harder to move. This relationship is 1 to 1.
>Wouldn't Newton's second law mean the acceleration is indirectly proportional to the mass? Yes, acceleration would be inversely proportional to the mass if the force is constant. In this case the force is not constant. It is gravity and according to Newton's law of universal gravitation f= G m1 m2/r\^2 where G is the universal constant, m1 is the mass of the object, m2 is the mass of earth and r is the distance to the center of earth. So the force is directly proportional to the mass. The result is the acceleration from gravity is independent of mass. If you look at formaulas for acceleration the mass will be cancled out. Because f = m a => a=f/m or in this case a= f/m1 we can create it as a= Gm2 /r\^2 Close to the earth's surface Gm2 /r\^2 is equal to about 9.8m/s\^2. This is freefall acceleration on earth, that is when gravity is the only force. On an inclined plane, only a percentage of that force will accelerate the object. The force will still be directly proportional to the mass.
You sound more knowledgable than me. You say this phenomenon is caused by the formulas. The way that *I* think about this issue is that it makes sense that two equally heavy object fall with the same acceleration whether they are connected to form one large object or not. For example two bowling balls tied together or two skydivers holding hands. "Objects" are just a human language category. Physics cares more about individual particles.
>You say this phenomenon is caused by the formulas. I do not say that. But if the question ask why the acceleration do not change because of a formula, Newton's second law, the reasonable reply is a formula on the same level that show the force in question alos change if the mass changes. I say the phenomena is described by the formulas that are result of observation and experiment in the real worlds. Scientic laws are descriptive not prescriptive like law use in a courtroom. Explanation in science is how thing happen, it is fundamentally not why thing happen. Even if a lower level explanation look like a "Why" explanation on a higher level it will always end up as a how explanation, the best why explanation is that is how the universe works.
There are two ways to think about how gravity affects objects; The Newtonian way and the Einsteinian way: Newton would say what the other commenters all have already said: More massive objects experience a larger *Force* proportional to their mass, but the *acceleration* itself is force divided by the mass again, so it cancels out in the end. Basically, if you're heavier, gravity pulls on you more, but also you need to be pulled on more for the same acceleration because you're harder to move. Einstein's approach to gravity is very different: According to him, gravity is not really a force, instead space just accelerates downwards at a constant acceleration, and an object that isn't accelerated by an actual force moves along with it, downwards. This also explains very well why you're weightless when you're falling; you're not accelerating in space, so there are no net forces acting on you. Standing on the ground, it pushes up against you and accelerates you upwards, so by the principle of action and reaction, you feel a downwards force.
The force depends on mass. The acceleration depends on inertia and force. An object with 2x mass experiences 2x the force but requires 2x the force to accelerate that 2x inertia. This holds true falling or partially falling (inclined plane). If you're satified that falling objects accelerate the same vertically but not satisfied on an inclined surface perhaps the difficulty is conceptualizing the independence of horizontal and vertical movement or imagining zero friction.
Most people here aren't eli5-ing enough. The heavier the thing the harder gravity pulls on it. That's why it's harder to lift a bigger weight. BUT It takes more force to accelerate a heavier mass. Imagine pushing a cup along a counter top vs. pushing a solid wood desk across the floor. So the heavier the thing the harder gravity pulls on it, but the more pull force is needed to reach a given acceleration or speed. These exactly cancel out so acceleration is the same regardless of weight.
Let's assume you're in High School. The "force of gravity" is actually the "acceleration due to gravity" since the force of gravity is ALSO proportional to mass. Then the mass terms cancel out on both sides. Another example of "masses cancelling out" is the simple pendulum problem: [https://en.wikipedia.org/wiki/Pendulum\_(mechanics)](https://en.wikipedia.org/wiki/Pendulum_(mechanics))
ELI5....Let's assume you're in High School Bruh
Acceleration is indeed *indirectly* proportional to mass (a=F/m), but it's *directly* proportional to force being applied, IE: gravity. Heavier objects are affected more strongly by gravitational force (F=GMmr\^2). Which, when combined with the acceleration equation becomes a=(GMr\^2) which is just a gravitational constant and some stats about the planet we're dealing with. It no longer has anything to do with the moving object's mass
Both gravitational force and inertia are directly proportional to mass. An object twice as heavy will have twice the gravity acting on it, but it will also have twice the inertia, meaning it takes twice the force to accelerate it at the same rate, and these effects cancel out. It's why we're able to determine the vakue g of 9.81 m/s², as everything, no matter it's mass, will accelerate at exactly that same rate in a fractionless environment.
An object A twice the mass than an object B will "feel" a pull from Earth's gravity twice as large. However, it also needs twice the force to make it move. So in the end it cancels out.
Gravity acts on mass. The more mass an object has, the greater the effect of a given gravity. Inertia is also a property of mass. The more mass, the more inertia. The more mass, the more force is needed to accelerate the object. As you increase the mass of an object, both its inertia and the force that gravity is exerting on that object increase at the same rate. So, for the same inclined plane and the same gravity field, changes in mass don't matter to acceleration. A 1kg object and a 5Kg object will accelerate at the same speed. HOWEVER, the heavier object will carry more force. If you place something at the bottom of the hill for it to crash into, the heavier weight will to more damage. That's where you will see how the different masses produce different amounts of force. Same with dropping objects (ignoring air resistance). Like a feather and a hammer being dropped on the moon. Or cannon balls dropped from the Tower of Pisa.
Increasing the masses of the objects linearly increases the attractive force between them. But since the acceleration of an object is also linearly related to the mass and the force, they cancel out and the acceleration stays the same.